Low complexity adaptive equalizer radio receiver employing direct reference state updates

ABSTRACT

A low complexity adaptive equalizer for use in U.S. digital cellular radios demodulates π/4-shifted differentially encoded quadrature phase shift keyed (DQPSK) encoding in the presence of intersymbol interference (ISI) with reduced decoding complexity by employing an estimated received constellation which takes into account channel changes over time and ISI. The decoding complexity is reduced by tracking a reduced number of estimated reference symbol constellation points and taking advantage of the geometry to estimate the remaining symbol constellation points. Reference symbol constellation points are updated directly to compensate for changes in the channel, instead of determining channel impulse response (CIR) coefficients, and convolving the CIR coefficients with received symbols to determine new reference symbol constellation points.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application is related to U.S. patent applications "A LowComplexity Adaptive Equalizer Radio Receiver Employing ReducedComplexity Branch Metric Calculation" by Sandeep Chennakeshu, RavinderDavid Koilpillai, Raymond Leo Toy Ser. No. 08/143,027, and "A LowComplexity Adaptive Equalizer for U.S. Digital Cellular Radio Receivers"by Sandeep Chennakeshu, Paul W. Dent, Ravinder David Koilpillai, RaymondLeo Toy Ser. No. 08/143,028, both filed concurrently herewith.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to mobile radio systems and more specifically totransmitting, receiving and demodulating digital information in adigital radio system.

2. Description of Related Art

In digital mobile radio systems, base units communicate with mobileradio units. Both base and mobile units employ a transmitter andreceiver. During communication, one of the communicating units transmitssymbols embedded in a continuous radio-frequency (RF) signal allowing areceiver to decode the RF signal into digital information. The motion ofthe mobile units causes impairments in the signal, or channelimpairments, known as Doppler shifts.

Transmitted signals may be received directly by the receiving unit as afirst ray, and also as a second ray which is reflected from a physicalobject. This is a channel impairment known as multi-path propagation.The second ray may arrive at the receiving unit slightly later due toits longer transmission path. This is known as delay spread.

Another channel impairment is known as intersymbol interference (ISI).Data symbols are usually filtered before transmission. This filteringcauses a symbol to have a duration that is longer than a symbol durationbefore filtering. ISI arises when a symbol overlaps onto a subsequentsymbol period and thereby affects the next transmitted symbol. ISIarises due to multi-path propagation and due to the nature of a filteredtransmitted symbol.

If the above channel impairments remain uncorrected, the received signalwhen demodulated could result in data with a high probability of error,causing a significant increase in bit error rate (BER) in the decodeddigital information. In order to improve the BER, an equalizer isemployed to demodulate the ISI-impaired received signal.

For the U.S. digital cellular system (IS-54), a time division multipleaccess (TDMA) system, the following mobile channel model has beenspecified in "Recommended Minimum Performance Standards for 800 MHzDual-Mode Mobile Stations", (incorporating EIA/TIA 19B), EIA/TIA ProjectNumber 2216, March 1991 for the purpose of evaluating the performance ofcandidate equalizer designs. The mobile channel is specified to be a tworay multipath model. Both rays are independently Rayleigh faded, withequal average power, and frequency shifted by a Doppler spreadcorresponding to the vehicle speed. The delay spread is defined in termsof a delay interval (τ) which is the difference in microseconds betweenthe first and last ray in the two ray channel model.

Any communications system for U.S. Digital cellular telephones must meetthe specified requirements on the channel model described above.Further, it is desirable that the mobile transmitter/receiver be small,(preferably hand-held), have low power consumption and be of lowcomplexity. The need for an equalizer in a cellular radio telephoneincreases the complexity and power drain. Hence there is a need todesign the equalizer for the above-mentioned application such that it isof low power, low complexity and will meet the performancespecifications of the U.S. digital cellular TDMA standard.

Non-linear equalization schemes such as decision feedback equalizationand equalization using maximum likelihood sequence estimation (MLSE) areconsidered appropriate for the above mobile channel. Decision feedbackequalizers (DFEs) present a powerful equalization scheme as described in"Decision Feedback Equalization for Digital Cellular Radio" by S.Chennakeshu, A. Narasimhan, J. B. Anderson, Proceedings ofICC,339.41-339.4.5, pp. 1492-1496,1990; and "An Adaptive LatticeDecision Feedback Equalizer for Digital Cellular Radio", Proceedings ofVTC, pp. 662-667, 1990 by A. Narasimhan, S. Chennakeshu, J. B. Andersonand can be very effective when used in conjunction with antennadiversity. However, they are usually too complex to implement in amobile receiver. The complexity is mainly due to the requirement for afast recursive least squares (FRLS) algorithm to estimate and track thechannel impulse response (CIR). Further, these approaches are prone toerror propagation and consequently high BER at higher vehicle speeds.

A DFE approach with a novel block-adaptive strategy is described in"Adaptive Equalization and Diversity Combining for a Mobile RadioChannel" by N. W. K. Lo, D. D. Falconer, A. U. H. Sheikh, Proceedings ofGlobecom, 507A.2.1-507A.2.5, pp. 923-927, 1990 wherein the time varyingCIR estimates are computed through interpolation between known CIRestimates. This scheme entails lower complexity than the aboveapproaches and eliminates the effect of error propagation, since thereis no decision directed estimation of the CIR. When used in conjunctionwith antenna combining this method has been shown to be very effective.However, in the U.S. digital cellular system the use of π/4-shiftedDQPSK modulation causes the CIR estimates to have phase ambiguities,which precludes direct application of the block-adaptive CIRinterpolation scheme.

Another problem with the DFEs is that they exhibit sensitivity to thenon-minimum phase condition in the channel, which occurs when the secondray is stronger than the primary ray. These limitations of the DFE makethe MLSE based algorithms preferable for use in mobile radio receivers.

An MLSE based receiver which may be used in U.S. digital cellular systemis disclosed in U.S. Patent Application "Adaptive MLSE-VA based Receiverfor Digital Cellular Radio" by S. Chennakeshu, A. Narasimhan, J. B.Anderson Ser. No. 07/753,578 filed Sep. 3, 1991, and now U.S. Pat. No.5,285,480. This MLSE based receiver is also relatively complex toimplement.

Analysis of the equalizer algorithm indicates that the complexity stemsfrom i). the branch metric computations, ii).CIR estimation and trackingwhich requires an adaptive algorithm, iii). the need for a CIRextrapolation scheme, due to the use of a large "decision depth"(usually greater than 5 symbols), especially at high vehicle speeds (>60Kmph). In view of the complexity of the computations, requiring morethan 5 million manipulations per second (MIPS) to run at a required datarate of 48.6 kilobits per second (Kbps), this MLSE based design limitsits use in smaller transceivers.

An alternate MLSE receiver implementation, entailing a computationalcomplexity requiring 9-10 MIPS is disclosed in "Receiver Performance forthe North American Digital Cellular System" by G. Larsson, B.Gudmundson, K. Raith, 41st Vehicular Technology Society ConferenceProceedings, pp. 1-6, St. Louis, Mo., May 1991. Although this MLSEreceiver satisfies the requirements of U.S. TDMA digital cellulartelephone system, the complexity is considered to be too high forimplementation in a mobile radio receiver. It is, however, a goodcandidate equalizer for the base station.

U.S. patent application "Adaptive Maximum Likelihood Demodulator" byPaul W. Dent Ser. No. 07/868,339 describes a method of demodulatingdigital information employing a maximum likelihood sequence estimator(MLSE) equalizer.

Currently there is a need for a simplified digital radio equalizer fordemodulating information encoded in a transmitter in accordance with theU.S. digital cellular standard (IS-54) and more generally, a need forrealizing a low complexity MLSE equalization technique for TDMA digitalradio transmissions over channels producing ISI.

OBJECTS OF THE INVENTION

An object of the present invention is to provide a communication systememploying a simplified equalizer in the receiver for time divisionmultiple access (TDMA) cellular systems.

Another object of the invention is to provide a hand-held communicationsystem for TDMA cellular telephone systems.

SUMMARY OF THE INVENTION

A digital communication system comprises a digital information sourcefor providing data symbols to be transmitted, a transmitter fortransmitting data symbols in a digital radio-frequency (RF) signal, anantenna for sensing the RF signal, a receiver employing an equalizer,and an output means for utilizing the decoded data symbols.

The receiver may be a mobile radio receiver or hand-held portable radioreceiver employing the method for demodulating π/4-shifted DQPSK data,which satisfies the minimum bit error rate (BER) performancerequirements of the TDMA based U.S. Digital Cellular system (IS-54).

The present invention is based on a maximum likelihood sequenceestimation (MLSE) approach and improves on the prior art by: i).reducing the number of computations in the branch metric, ii). directlyupdating estimated received symbol constellation points by an improvedtechnique, iii). employing information previously calculated from symbolcomputations for branch metrics, iv). employing an improved gradientalgorithm for updating signal states, v). elimination of extrapolationof CIR estimates employed in prior art receivers, and vi) decodingpartial segments in forward and reverse directions.

The present invention satisfies the bit error rate (BER) specificationsof the Cellular Telecommunications Industries Assoc. (CTIA), has a lowcalculation complexity requirement of approximately 3 MIPs for therequired data transmission rate. Further, the complexity of the methodof the present invention can be reduced to approximately 1.5 MIPS forimplementation in a hand-held portable radio.

The equalizer is designed to be enhanced by bi-directional decoding ofdata slots in partial forward and reverse directions in order to isolatea fade period and enhance performance.

BRIEF DESCRIPTION OF THE DRAWINGS

The features of the invention believed to be novel are set forth withparticularity in the appended claims. The invention itself, however,both as to organization and method of operation, together with furtherobjects and advantages thereof, may best be understood by reference tothe following description taken in conjunction with the accompanyingdrawings in which:

FIG. 1a is a graphic representation of an even symbol constellation forπ/4-shifted differentially encoded quadrature phase shift keying(DQPSK).

FIG. 1b is a graphic representation of an odd symbol constellation forπ/4-shifted differentially encoded quadrature phase shift keying(DQPSK).

FIG. 2a is an estimated encoder state change diagram over time havingfour states, commonly referred to as a trellis state diagram.

FIG. 2b is a diagram of one stage of a trellis state diagram having fourstates corresponding to a single transmitted symbol.

FIG. 3 is an illustration of data transmission format for time divisionmultiplexed access (TDMA) U.S. Digital Cellular telephone IS-54 baseunit to mobile unit.

FIG. 4a is a diagram of an estimate of possible received symbolsincorporating intersymbol interference from a previously transmittedsymbol when an even π/4-shifted DQPSK constellation symbol istransmitted.

FIG. 4b is a diagram of an estimate of possible received symbolsincorporating intersymbol interference from a previously transmittedsymbol when an odd π/4-shifted DQPSK constellation symbol istransmitted.

FIG. 4c is an illustration of the relative gains of a primary symbol andan interfering previously transmitted symbol.

FIG. 5 is simplified block diagram of a digital radio communicationsystem according to the present invention.

FIG. 6 is a graph of bit error rate (BER) vs. a ratio of carrier tointerference (C/I) power in decibels (dB).

DETAILED DESCRIPTION OF THE INVENTION

Received Signal with ISI

As mentioned above, ISI is the superposition of a previously transmittedsignal onto the present symbol. This can be represented in an equationfor a received signal sample r[n] being a digital approximation of theanalog received signal r(t):

    r[n]=h.sub.0 [n]s[n]+h.sub.1 [n]s[n-1]                     (1)

where h₀ [n] and h₁ [n] are time-varying channel coefficients withcomplex gains each having a phase and an amplitude which describetransmission through a channel and s[n] represents the actualtransmitted data. In the U.S. digital cellular telephone standardsreferenced above, a two-ray model for intersymbol interference isemployed, which is the same model employed here, denoted as:

    r[n]=h.sub.0 [n]s[n]+h.sub.1 [n]s[n-1].                    (2)

Transmission

In π/4-shifted differential quadrature-phase shift keying (π/4-shiftedDQPSK), symbols are transmitted alternately as a phase angle from aneven symbol constellation, as shown in FIG. 1a, then from odd symbolconstellation, as shown in FIG. 1b. If the last symbol sent s[n] wasfrom the even symbol, then the previous symbol s[n-1] was chosen fromodd symbol constellation. The symbols of the even constellation may bedenoted as {S} and those of the odd constellation may be denoted as {S},with j, i representing the symbol index of a symbol chosen from the evenand odd constellations denoted as s_(j) [n] and s_(i) [n], respectively.

Symbol Decoding

In prior art methods of equalizing and decoding of signals, after thesymbols are transmitted to a receiver, an exhaustive search for symbolss[n] is executed which minimizes a path metric, being a sum of allbranch metrics, each representing a Euclidian distance (squared) betweenreceived signal samples and an estimate of the received samples givenby: ##EQU1##

The estimated received signal samples are a convolution of theperturbation which occurs during transmission through the channel,defined by channel coefficients h₀ [n], h₁ [n], and the symbols s[n],s[n-1] which were originally transmitted. The intent is to obtain theoriginal transmitted symbols s[n] from the received symbols r[n]. Amaximum likelihood sequence estimation (MLSE) scheme, such as a Viterbialgorithm, may be implemented in decoding π/4-Shifted-DQPSK encodeddigital information as described in "Viterbi Algorithm", Proceedings ofthe IEEE, Vol. 61, pp. 268-278, March 1973; and MLSE type decoders asdescribed in "An Adaptive MLSE Receiver for TDMA Digital Mobile Radio",by R. D'Avella, et al, IEEE Journal on Selected Areas in Communications,Vol. 7, No. 1, January 1989, pp. 122-129. This scheme performs thesearch to find best symbols sequence {s[n]} that minimizes the abovepath metric.

To understand the method of demodulating received symbols similar tothat executed by the Viterbi algorithm, an encoder state change diagramover time is required. In the problem considered herein, the encoderrefers to ISI produced by the channel since the channel transforms asingle transmitted symbol into a received symbol with ISI. For purposesof illustration, the transmitter and channel may be represented as asingle encoder that produces the received signal described by Eq. (1).This type of encoder state diagram is commonly referred to as a trellisdiagram. FIG. 2a illustrates a simple trellis for an ISI problemgenerated by a two ray channel. The following are assumed: there are twochannel impulse response (CIR) coefficients h₀ [n], h₁ [n], and eachtransmitted symbol can take 4 values. The trellis shown in FIG. 2aillustrates the possible states of an encoder (transmitter and channel)and the progression of a sequence of states over time, shown by pathsthrough the trellis. Each possible state transition has beenpre-assigned to a transmitted symbol in the construction of the encoder.As the encoder receives information, it changes encoder states andtransmits symbols corresponding to these assigned state changes. Eachstate at a specified time (or "stage") is defined as a node. At eachtime instant, there are 4 nodes in the trellis; therefore, this systemis known as a "4 state trellis". There are branches that connect nodesfrom one time instant to the next. A branch is specified by a symbolpair denoted by {s[n],s[n-1]}. A continuous set of these branches,referred to as a path through the trellis, signifies a possiblecombination of symbols that can be transmitted.

A temporary assumption is made that the values of h₀ [n], h₁ [n] areknown for all time instants n. A metric or "weight" can be assigned toeach branch or transition employing h₀ [n],h₁ [n] and the symbol pair{s[n],s[n-1]} associated with each branch. This "branch metric"corresponding to n^(th) time instant is defined as:

    d.sub.ji (n)=|r.sub.n -{h.sub.0 [n]s.sub.i [n]+h.sub.1 [n]s.sub.j [n-1]}|.sup.2                                    (4)

The above definition represents the "branch metric" corresponding to thebranch from node "j" at time n-1, to node "i" at time n. This branchmetric signifies a measure of distance between the actual receivedsignal sample to the estimation of the received signal sample {h₀[n]s_(i) [n]+h₁ [n]s_(j) [n-1]}. The branch metrics for all branches ofa path through the trellis are accumulated to result in a "path metric"P_(i) for a path ending on state "i". The sequence of symbols {s[n]}along the path through the trellis with the lowest path metric P_(min),is the maximum likelihood sequence.

There are numerous possible paths through the trellis. It is onlynecessary to retain as many path metrics as there are nodes. In thepresent example, the number of path metrics is 4.

With the above definitions, the Viterbi method may be described as amaximum likelihood recursive technique that decodes symbols by tracingan optimal path of symbols through the trellis.

FIG. 2b illustrates one stage of the recursion. Four branches fromstates 0,1,2,3 at time n-1 to state 0 at time n. Each of these branchesuniquely specifies a symbol pair {s[n-1], s[n]} and hence represents aunique "length" or "distance" computation for each path segment fromstate j at time n-1 to state i at time n corresponding to a Euclidiandistance from a received symbol and estimated a symbol constellationpoint from {Z} or {Z}. Each of the four distances are computed, namely,{d₀₀ (n),d₂₀,d₁₀ (n),d₃₀ (n)} according to Eq. (4). Next, theaccumulated path distances, namely {P₀ (n-1)+d₀₀ (n)}, {P₁ (n-1)+d₁₀(n)}, {P₂ (n-1)+d₂₀ (n)}, {P₃ (n-1)+d₃₀ (n)}, are computed correspondingto distances up to the state 0 at time n. Then the minimum of the fouraccumulated distances is chosen. This becomes the new path metric P₀(n).

The transition from state j at time n-1 to state i at time n thatproduced this minimum path metric (corresponding to the most probablestate) is stored. The connected transitions or branches that produce theminimum path metric up to a certain point in time in the trellis isreferred to as the "path history". A register, referred to as^(PH).sbsp.n.sup.(i), exists for each node where n is a symbol periodnumber or trellis stage number, and i is a state number of the initialstate. The value store in each register indicates a transition from thepresent state to the most likely state in the previous symbol period.Stated differently, the register simply points from the current state iat time n to the previous state j at time n-1 which produces the minimumEuclidian distance among the 4 possible branches from state j at timen-1 to state i at time n. Hence, the path history serves to remember orindex the path branches that contribute to the best overall path.

In a similar manner the new path metrics and path histories are computedand stored for states 1,2,3 at time n. The above recursive computationfor the n^(th) stage of the trellis can be expressed symbolically as:##EQU2## Store state j for time n obtained in Eq. (5a) in register^(PH).sbsp.n.sup.(i). (5b)

The above recursion is performed for each stage of the trellis. Therewill be as many stages as transmitted symbols. At the end of the trellisall the accumulated path metrics P_(i) (N), i=0,1,2,3 are compared andthe minimum is chosen.

Next, starting from the last state of the path corresponding to thisminimum path metric, the path from this node is traced backward in timeusing the path history pointers ^(PH).sbsp.n.sup.(i). The symbolscorresponding to state transitions which occur during trace back aretaken to be the decoded sequence. (Recall that each node corresponds toa possible symbol value). This trace-back process may be expressedthrough the following sequence of operations: ##EQU3## start with statei corresponding P_(min) (6b)

set symbol period n=N (6c)

read ^(PH).sbsp.n.sup.(i) to locate node j at symbol time n-1(6d)

store symbol corresponding transition from nodes j→i at symbol timesn-1→n (6e)

set symbol period n=n-1 (6f)

set state i=j and repeat (6d)-(6f) recursively until starting node(n=1)(6g)

The above procedure, comprising Eqs. (3-6), comprise the method similarto that employed by the Viterbi algorithm. This method may be summarizedas follows:

Step 1

Initialize all path metrics P_(i) (0), i=0,1,2, . . . , M-1 to zero,where M is the number of possible states.

If the starting state is known, the path metric corresponding to thisstate is set equal to zero and all other path metrics are set to a largepositive number.

set time n=1

Step 2

compute the accumulated path metric ##EQU4##

Step 3

For each state i at symbol time period n, store the state transition(i→j) that produces the minimization in step 2, in a path history^(PH).sbsp.n.sup.(i) memory register. If N is the number of symbolperiods, there will be M×N path history memory registers, denoted by:

PH_(n) (0), PH_(n) (1), . . . , PH_(n) (M); where n=1,2,3, . . . , N

Step 4

Increment n=n+1 and repeat step 2 and step 3 until n=N

Step 5

Find ##EQU5## and store index i corresponding to minimum accumulatedpath metric.

Step 6

Trace back and decode symbols as follows:

a) start with state i corresponding to ##EQU6## of previous step; b) setsymbol period n=N;

c) read PH_(n) (i) to locate node j at symbol time n=1;

d) store symbol corresponding transition from nodes j→i at symbol timesn-1→n;

e) set symbol period n=n-1; and

f) set state i=j and repeat steps c) d) and e) recursively untilstarting node (n=1).

The concept of decision depth is used very frequently with the Viterbialgorithm. Usually, it is seen that after following the trellis for acertain length, say n stages and tracing back to a distance δ stages andit is determined that all paths at time n-δ have a common state. Thisimplies that up to time n-δ there is a single path that maybe taken tobe the best. This means that at time n-δ a firm decision may be made asto what the symbol is at that time. This circumvents the need totraverse the whole trellis before tracing back and then deciding uponthe symbols. The depth or distance n-δ used for making our decision on adecoded symbol is known as "decision depth".

The channel impulse response (CIR) coefficients h₀ [n], h₁ [n] arerequired to determine the estimated received symbols and minimize thebranch metric equation Eq. (4) and must be estimated over known symbols,such as a set of synchronization or ("sync") symbols which aretransmitted during each slot of data. FIG. 3 is a standard data formatfor U.S. cellular telephones for Base to Mobile communications. The syncsymbols may be from preamble bit positions 1 to 14 or a coded digitalverification color code (CDVCC) 47, bit positions 86 to 91 of a slot ofdata 40 as shown in FIG. 3. The remaining portions of slot 40 are theslow associated control channel (SACCH) information 43, bit positions 15to 20, data sections 45, 49 bit positions 21 to 85, and 92 to 155,respectively, for the message data and reserved bits, bit positions 156to 162. There are three slots per frame in this format.

Also, since channel coefficients h₀ [n], h₁ [n] change over time, theymust be updated or interpolated periodically. This also becomescomputationally burdensome, and may be too complex to implement in ahand-held transmitter/receiver.

Decoding: Present Invention

Since π/4-shifted DQPSK symbols are transmitted as a phase angle in analternating fashion, as shown in FIGS. 1a, 1b, ISI will result from thepreviously transmitted symbol s[n-1], being from the opposite symbolconstellation (odd vs. even) as the presently transmitted symbol s[n].FIG. 4a illustrates possible received symbols for the last receivedsymbol being from the even constellation, and FIG. 4b for the oddconstellation when the relative amplitudes are specified as shown inFIG. 4c. This is the result of vector addition of h₀ [n] s[n] and h₁ [n]s[n-1], having symbols 0, 1, 2, 3 for symbol n and symbol n-1 adjustedby channel coefficients h₀ [n] h₁ [n] to result in 16 possibilities. Anew term will be defined which is the vector sum of h₀ [n] s[n] and h₁[n] s[n-1] denoted as the estimated symbol constellation points {Z} forthe even constellation and described by:

    Z.sub.ji =h.sub.O s.sub.i [n]+h.sub.1 s.sub.j [n-1] for i,j=0,1,2,3(7a)

where s[n] takes on one of the values of the even π/4-shifted DQPSKsymbols and s[n-1] takes on one of the values of the odd π/4-shiftedDQPSK symbols.

The corresponding estimated symbol constellation points are describedby:

    Z.sub.ji =h.sub.0 s.sub.i [n]+h.sub.1 s.sub.j [n-1] for i,j=0,1,2,3(7b)

where s[n] takes on one of the values of the odd π/4-shifted DQPSKsymbols and s[n-1] takes on one of the values of the even π/4-shiftedDQPSK symbols.

Symmetry

By analyzing the symmetry of FIGS. 4a and 4b it is apparent that Z₁₁ isZ₀₀ shifted by π/2 or multiplied by e^(j)π/2, and Z₂₂ =Z₀₀ shifted bye^(j)π etc. The 16 possible states of FIG. 4a may be represented by fourreference states and appropriate phase shifts. Similarly, the 16possible states of FIG. 4b may be represented by four reference stateswith appropriate phase shifts. The relations may be grouped as follows:

Group 0

Z₀₀ (n)

Z₁₁ (n)=Z₀₀ (n)e^(j)π/2

Z₂₂ (n)=Z₀₀ (n)e^(j)π

Z₃₃ (n)=Z₀₀ (n)e^(j3)π/2

Group 1

Z₀₁ (n)

Z₁₂ (n)=Z₀₀ (n)e^(j)π/2

Z₂₃ (n)=Z₀₀ (n)e^(j)π

Z₃₀ (n)=Z₀₀ (n)e^(j3)π/2

Group 2

Z₀₂ (n)

Z₁₃ (n)=Z₀₂ (n)e^(j)π/2

Z₂₀ (n)=Z₀₂ (n)e^(j)π

Z₃₁ (n)=Z₀₂ (n)e^(j3)π/2

Group 3

Z₀₃ (n)

Z₁₀ (n)=Z₀₃ (n)e^(j)π/2

Z₂₁ (n)=Z₀₃ (n)e^(j)π

Z₃₂ (n)=Z₀₃ (n)e^(j3)π/2

There may be some confusion with regard to the use of the lower caseletters "j" and "j". The letter "j" (italics) signifies the complexoperator while the letter "j" (non italicized) signifies the index of astate. This point should be noted throughout the specification.

Similarly, from FIG. 4b we can form a set of relationships for the oddconstellation. The relationships are identical to the above set and isobtained by replacing all Z_(ji) (n) by Z_(ji) (n).

From the above relationships we notice that the entire set of 16constellation points can be derived from the basic set of estimatedreference symbol constellation points given by {Z₀₀ (n), Z₀₁ (n),Z₀₂(n)Z₀₃ (n)}. All other estimated symbol constellation points can beobtained by rotations of these 4 basic quantities by π/2, π and 3π/2radians as indicated above. (Note: e^(j)π/2 represents a rotation in thecounter-clockwise direction by π/2 radians and e^(-j)π represents arotation by π radians in the clockwise direction.)

Hence, we store only 8 basic signal constellation points, instead of 32points, corresponding to two constellations, namely, {Z₀₀ (n),Z₀₁(n),Z₀₂ (n)Z₀₃ (n)} and {Z₀₀ (n),Z₀₁ (n),Z₀₂ (n)Z₀₃ (n)}. The estimatedreference symbol constellation points may be labelled as follows:

(Even) Reference Symbol Constellation Points (States)

Z₀ ^(ref) (n)=Z₀₀ (n)

Z₁ ^(ref) (n)=Z₀₁ (n)

Z₂ ^(ref) (n)=Z₀₂ (n)

Z₃ ^(ref) (n)=Z₀₃ (n)

(Odd) Reference Symbol Constellation Points (States)

Z₀ ^(ref) (n)=Z₀₀ (n)

Z₁ ^(ref) (n)=Z₀₁ (n)

Z₂ ^(ref) (n)=Z₀₂ (n)

Z₃ ^(ref) (n)=Z₀₃ (n)

As mentioned earlier, there is a relationship between these two basicsets of constellation points which can be represented as:

    Z.sub.m.sup.ref (n)=Z.sub.k.sup.ref (n)e.sup.jπ/4

where m=(k+3) mod 4 and k=0,1,2,3 (8a)

    Z.sub.k.sup.ref (n)=Z.sub.m.sup.ref (n)e.sup.-j π/4

where k=(m+1) mod 4 and m=0,1,2,3 (8b)

CIR estimation

The basic quantity used in the metric computations are the referencestates, namely, {Z^(ref) }, {Z^(ref) }. An initial estimate of thesequantities is required to decode subsequent received signal samples.These estimates are obtained by estimating the CIR coefficients h₀ [n],h₁ [n] and convolving the estimated CIR with the correspondinghypothesized symbols.

The CIR estimate is obtained as a solution to a least squares problem.This estimation problem can be stated as follows:

find h₀ [n],h₁ [n], . . . ,h_(L-1) [n] such that ##EQU7## is minimized,where N_(p) corresponds to the number of sync symbols in preamble orCDVCC.

The exact solution to Eq. (9) can be written in matrix form as follows:

    h=[S.sup.H S].sup.-1 S.sup.H R                             (10)

where S^(H) is defined as S^(H) =[S^(T) ]*, h=[h₀ [n] h₁ [n] . . .h_(L-1) [n]]^(T),

R=[r₁ [n] r₂ [n] . . . r_(N).sbsb.P [n]] and the matrix S is given by:##EQU8##

The matrix given by Eq. (11) comprises symbols of the preamble. Hence,the matrix defined as M=[S^(H) S]⁻¹ S^(H) can be pre-computed. Usingthis definition the CIR can be estimated by a matrix multiplication asfollows:

    h=MR                                                       (12a)

A two ray channel is assumed (as per the IS-54 standard) and hence,there are only two CIR coefficients which are labeled as h₀ [n],h₁ [n].

The CIR coefficients h₀ [n],h₁ [n] obtained through Eq. (12a) may benoisy and may be refined by the following a smoothing scheme, which isrealized by implementing equations Eq. (12b-12e) in an iterative loopfor n=1,2, . . . ,N_(p).

    e(n)=r(n)-h.sup.T [n]S[n]

where h^(T) =[h₀ [n] h₁ [n]] and S^(T) [n]=[s_(pre) [n] s_(pre) [n-1]](12b)

    h[n+1]=h[n]+0.5e(n)S*[n]                                   (12c)

where S*[n] is the complex conjugate of S[n]. ##EQU9## whereσ(n)=λσ(n)+1; σ(0)=0; λ=0.6-1.0(12e)

σ is a weighting factor.

h=[h₀ [n]h₁ [n]]^(T) is a smoothed version of the CIR coefficients h.

The reference signal constellation (even) points can be obtained asfollows:

    Z.sub.i.sup.ref =h.sub.0 [n]s.sub.i +h.sub.1 [n]s .sub.0 ; for i=0,1,2,3(13)

where {h₀ [n]h₁ [n]} have been smoothed over the number of sync symbolsN_(p).

It is noted that for a π/4-shifted-DQPSK signal s_(i), i =0,1,2,3represents the four symbols, ##EQU10## constellation and s₀ representsthe symbol 1+j0 which is from the odd constellation.

Similarly, the reference signal constellation points corresponding tothe odd constellation resulting in:

    Z.sub.i.sup.ref =h.sub.0 [n]s.sub.i +h.sub.1 [n]s.sub.0 ; for i=0,1,2,3(14)

For a π/4-shifted-DQPSK signal s_(i), i=0,1,2,3 represents the foursymbols, {1,j,-1,-j}, from the odd constellation and s_(o) representsthe symbol ##EQU11## which is from the even constellation.

Simplified Computation of Branch Metrics

Using the above definitions for signal points, the number ofcomputations in the branch metrics of Eq. (4) may be simplified asfollows:

The branch metric for a trellis stage corresponding to an even symboltransmitted, can be written as:

    d.sub.ji (n)=|r.sub.n -Z.sub.ji (n)|.sup.2(15)

where Z_(ji) are defined previously.

However, since only four of the sixteen values of Z_(ji) (n) are stored,Eq. (9) must be expressed in terms of the four basic reference states{Z^(ref) }. Equation (15) can be rewritten as:

    d.sub.ji (n)=|r[n]-Z.sub.k.sup.ref (n)e.sup.jπ/2*j |.sup.2                                          (16)

where k=(i+3j) mod 4 and i,j=0,1,2,3. Eq. (16) can also be written as:

    d.sub.ji (n)=|r.sub.n e.sup.-jπ/2*j -Z.sub.k.sup.ref (n)|.sup.2                                       (17a)

where k=(i+3j) mod 4 and i,j=0,1,2,3.

Similarly, the branch metric for a trellis stage corresponding to an oddsymbol transmitted can be written as:

    d.sub.ji (n)=|r[n]e.sup.-jπ/2*j -Z.sub.m.sup.ref (n)|.sup.2                                       (17b)

where m=(i+3j) mod 4 and i,j=0,1,2,3. From Eqs. (16), (17a) and (17b) itbecomes apparent that each distance value d_(ji) (n) can be computed byrotating one of the four stored reference states {Z} or {Z} in acounterclockwise direction by an integral multiple of 90 degrees (modulo360 degrees), or by rotating the received signal in a clockwisedirection by an integral multiples of 90 degrees (modulo 360 degrees).The latter is more efficient as it entails only four complex multiplies(rotations), while the former entails sixteen complex multiplies(rotations).

Further, simplifications in computation of branch metrics can beachieved by grouping distance computations and avoiding repetitions incomputations. To illustrate this four groups of distances are formed asfollows:

Group 0

{d₀₀ (n),d₁₁ (n)d₂₂ (n)d₃₃ (n)}

Group 1

{d₀₁ (n),d₁₂ (n)d₂₃ (n)d₃₀ (n)}

Group 2

{d₀₂ (n),d₁₃ (n)d₂₀ (n)d₃₁ (n)}

Group 3

{d₀₃ (n),d₁₀ (n)d₂₁ (n)d₃₂ (n)}

Z_(k) ^(ref) (n) and Z_(m) ^(ref) (n) may be expressed in Cartesian formas:

    Z.sub.k.sup.ref (n)=a.sub.k (n)+jb.sub.k (n)

    Z.sub.m.sup.ref (n)=a.sub.m (n)+jb.sub.m (n)

Further, let message symbols r_(sp) [n]=I[n]+j Q[n]. Hence, from Eq. (4)distances can be computed within a group as:

Distance Calculation for Group 0

    d.sub.00 (n)=I.sup.2 [n]+Q.sup.2 [n]+a.sub.0.sup.2 (n)+b.sub.0.sup.2 (n)-2(a.sub.0 (n)I[n]+b.sub.0 (n)Q[n])

    d.sub.11 (n)=I.sup.2 [n]+Q.sup.2 [n]+a.sub.0.sup.2 (n)+b.sub.0.sup.2 (n)-2(a.sub.0 (n)Q[n]-b.sub.0 (n)I[n])

    d.sub.22 (n)=I.sup.2 [n]+Q.sup.2 [n]+a.sub.0.sup.2 (n)+b.sub.0.sup.2 (n)+2(a.sub.0 (n)I[n]+b.sub.0 (n)Q[n])

    d.sub.33 (n)=I.sup.2 [n]+Q.sup.2 [n]+a.sub.0.sup.2 (n)+b.sub.0.sup.2 (n)-2(a.sub.0 (n)Q[n]+b.sub.0 (n)I[n])

The corresponding distances for all other groups can be calculated asshown above. Scaling the above distances by a constant does not alterthe optimization criterion of Eq. (5a). Hence, the above distances maybe scaled by a factor of 1/2. Further, the term I² [n]+Q² [n] is aconstant for all 16 distance computations and can be eliminated from thecomputations. This term represents the instantaneous power in thereceived signal.

Scaling the distances by a factor of 1/2 and eliminating the receivedpower term I² [n]+Q² [n] the 16 distances (branch metrics) can bewritten as: ##EQU12##

The corresponding branch metrics for the odd symbol constellation aregiven by replacing "a" with "a" and "b" with "b", and "d" with "d",where "a,b" are the complex components of odd symbol constellationpoints {Z} "d" is the Euclidian distances between the received messagesymbol r_(sp) [n] and each odd symbol constellation point.

The above branch metric expressions can be computed using a total of 56operations (28 multiplies and 28 adds). The "brute-force" method ofcomputation represented by Eq. (16) requires 80 operations (32multiplies and 48 adds) to compute all 16 branch metrics. Hence, theabove method provides a saving of 24 operations per trellis stage. Thistranslates to a saving of 3408 operations per data slot (142 symbols).

Additional Savings in Computations

An additional savings of 12 operations per stage can be achieved bystoring the values of coefficients X_(i), ##EQU13## for those "i" statesthat are not updated. In a preferred embodiment, only one state isupdated per trellis stage. This provides a reduction in the number ofoperations per stage from 56 to 44. The total savings is 4684 operationsper data slot.

It is to be noted that the above branch metrics can be computed in Polarco-ordinates to provide an additional saving of 4 operations, pertrellis stage, over the Cartesian method. However, the Polar methodentails a higher complexity in the overall algorithm, mainly due toCartesian to Polar conversions, and is considered only as analternative.

Update Method 1 (No Decision Depth)

The reference signal updating mechanism can now be explained as follows.Let us consider that the trellis search has progressed up to an evenstage, for example stage n. At stage n the path metrics P₀ (n), P₁ (n),P₂ (n) are compared and the minimum is chosen. Taking, for example, theminimum being P₁ (n). Next, record the branch or transition from state jat stage n-1 to state 1 at stage n. Assume that this transition j→1corresponds to the transition from state 2 (i.e. j=2) at stage n-1 tostate 1 at stage n. Recall that each transition in a trellis stagedefines one of the reference signal constellation points. In thisexample the 2→1 transition defines the reference signal Z.sub.(i+3j)mod4^(ref) (n)=Z.sub.(1+3*1)mod 4^(ref) (n)=Z₀ ^(ref) (n). This referencestate is then updated according to the following rule: ##EQU14## wherek=(1+3j) mod 4, D represents the delay corresponding to the last timethis reference signal constellation point was updated, γ is a timeconstant that determines the rate of adaptation and noise variance, γ ischosen to be a value between 0 and 1. The value γ=0.7 was found to beoptimal for our specific application. The received message sample r_(sp)[n] must be rotated in a clockwise direction by π/2*j degrees, where jis then obtained from the j→i transition recorded. Note, that thisrotation is done during the computation of branch metrics and need notbe repeated in Eq. (18a).

In the above scheme, a reference state is updated every alternate stage.Since there are 4 odd and 4 even reference signal points, this impliesthat each reference signal point will be updated on an average every 8thsymbol time. The period between symbol updates may be reduced to onceevery 4th symbol time period by using the relationships specified inEqs. (8a) and (8b). That is, if an even reference state is updated viaEq. (18a), a corresponding odd reference signal may be updated using Eq.(8a). Similarly, if an odd reference state is updated, an even referencestate may be updated using Eq. (8b). The rotations implied by Eqs. (8a)and (8b) may be performed in Polar form or Cartesian form as follows:##EQU15## where {I_(k), Q_(k) } are the complex components of Z_(k)^(ref) (n).

The updating procedure at odd stages in the trellis is identical to theabove procedure outlined for even stages. Only now, the odd referencesignal states are updated according to Eq. (18a) and the correspondingeven reference state is updated by a 45 degree rotation as specified inEq. (8b). The corresponding update equations for odd stage of thetrellis is: ##EQU16## where m=(i+3j) mode 4; with the correspondingsecondary even reference symbol being updated from the odd symbolaccording to: ##EQU17## where {I_(m), Q_(m) } are the complex componentsof Z_(m) (n).

Updating Method 2 (Decision Depth)

In the above updating method a decision to update a state is made basedon the accumulated path metric at the stage in the trellis. Thisdecision tends to be unreliable during poor SNR conditions. The conceptof decision depth could be used to improve reliability of decodingsymbols. The same concept can be used to update the reference states. Inthis method the state corresponding to the minimum path metric is chosenand starting from this state the trellis is traced backwards by a numberof symbols corresponding to the decision depth (δ). The resulting stateis more reliable than the state which would have resulted withoutdecision depth. This state is used as reference state (i) for thepreviously described Update Method 1. Note that Update Method 1 isessentially the same as Update Method 2 with a decision depth of 0.

Some subtleties in implementing the above technique must be observed.First, a time delay of δ must be included in Eqs. (18a) and (19a) whichimplies subtracting δ from n and D. Now, the estimate of the referencesignal state lags the true value by a delay δ. Secondly, when thetrellis is traced back an odd number of stages, by δ=1,3,5 . . . , theresult is an odd stage if we start from an even stage. Hence, an oddreference symbol is updated first using Eq. (19a), and then Eq. (19b) isused to update the corresponding even reference signal point. Forδ=0,2,4, . . . , an even number of stages are traced back and the updateequations given Eqs. (18a) and (18b) are used.

One of the most important considerations in the implementation of thisscheme is the choice of δ is a tradeoff. Larger δ implies more reliablestate decisions but larger time lag. The larger time lag implies asmaller correlation between the true reference signal value and theestimated value if the channel is fading very rapidly. The δ value ofδ=1 was found to be optimal for the best embodiment when using theupdate equations Eqs. (18a, 18b, 19a, 19b).

FIG. 5 is a simplified block diagram of an apparatus capable ofperforming the method the present invention. A digital informationsource 1 provides information desired to be transmitted through achannel, known as message information. This is combined with requiredsynchronization information such as a preamble 41 or CDVCC 47 of FIG. 3.

Transmitter 3 then transmits the digital information, such as symbolsfrom π/4-shifted differential quadrature phase shift keying (DQPSK) fromalternating even, odd symbol constellations on a radiofrequency carriersignal. This signal is received and heterodyned to an intermediatefrequency (IF) signal by a down converter 5.

The IF signal is sampled by an analog-to-digital (A/D) converter 7 toprovide received samples r[n], where n relates to the time the samplewas acquired.

A synchronization unit ("sync unit") 9 synchronizes the signal andseparates the received samples into samples relating to sync samplesr_(pre) [n], and message samples r_(sp) [n] and retains both for furtherprocessing.

An initial channel impulse response (CIR) estimation unit 11 receivesthe sync samples r_(pre) [n], and is provided with the samepredetermined sync symbols s_(pre) [n] which were combined with themessage data before transmission at the transmitter. The CIR estimationunit provides initial values of the CIR coefficients {h₀ h₁, . . . , }.An initial reference symbol unit receives the initial CIR coefficients{h₀, h₁, . . . , }, and the known sync symbols s[n], the received syncsamples r_(pre) [n] and constructs initial values of estimated symbolconstellation points Z, Z. Each estimated symbol constellation point isan approximation of the possible resulting points which would occur fromdiffering combinations of transmitted symbols taking into accountintersymbol interference from a previously transmitted symbol, and thecurrent CIR. This may be computed by determining the CIR by aconventional method, then employing Eq. 13. In a preferred embodiment,the CIR coefficients are calculated through Eqs. 12b through 12d, andthen employed in Eq, 13 to determine the initial symbol constellationpoints {Z}, {Z}.

An equalizer 20, comprised of a reference symbol update unit 21, and amaximum likelihood sequence estimator (MLSE) decoder 23 equalizes thesignal and decodes the symbols. MLSE decoder receives the messagesamples r_(sp) [n] and the symbol constellation points {Z}, {Z} (initialvalues for the first stage and updated values for subsequent stages).The MLSE decoder decodes a phase angle Δφ corresponding to the messagesample r_(sp) [n] and passes this phase to reference symbol update unit21 which updates a portion of the estimated symbol constellation points{Z}, {Z} according to Eqs. (18a, 18b, 19a, 19b). The estimated symbolconstellation points {Z}, {Z} are fed back to MLSE decoder 23 to resultin further message symbols being decoded. The decoded phase angles Δφare sent to a phase to bit mapper which converts each decoded phaseangle to a bit sequence in the same fashion as when the information wasfirst transmitted. This process is repeated for all symbols in a slotand the entire process is repeated starting from the calculation of newinitial values for CIR coefficients and estimated symbol constellationpoints {Z}, {Z} for each new set of sync symbols.

The equalizer of the present invention is specially matched to themethod of decoding disclosed in U.S. patent application "Double SidedSlot Traversing (DSST) Decoding for TDMA Systems" Ser. No. 08/039,599filed Mar. 29, 1993 by S. Chennakeshu, R. Koilpillai and R. Toy whichdescribes dividing the sampled signal into halfslots of samples. Thehalfslots are subdivided into subslots numbered from 1 to N_(SL), whereN_(SL) represents the last received subslot. Subslots 1 and N_(SL) aredemodulated into digital information in a forward and reverse direction,respectively with metrics calculated. If the metrics indicate a signalwith a larger signal-to-noise ratio from subslot N_(SL), subslot N_(SL)-1 is demodulated in a reverse sense with another reverse metriccalculated, and vice versa. This process of extending demodulation inthe direction of greater signal strength is repeated until all subslotsin the slot have been demodulated. This method of decoding isspecifically resistant to fades and is the preferred sequence ofdecoding for the present invention.

Specifically, the present invention is applicable to π/4-shifted DQPSK,and π/4-shifted QPSK and may be applied to digital cellularradiotelephone and land mobile radio equipment. There is also apotential application to personal communications systems (indoor andmicrocellular). The present invention is also applicable to wireless orcellular secure telephone units (STU's) and military radios. In all ofthe stated applications, this invention can be applied also to basestations.

FIG. 6 is a graph of a simulation illustrating the performance of thepresent invention. For a mobile unit speed of 100 kilometers/hour, thebit error rate (BER) is graphed against the ratio of carrier tointerference (C/I) power in decibels (dB). Tau (τ) is the relative gainof an interfering ray.

While several presently preferred embodiments of the invention have beendescribed in detail herein, many modifications and variations will nowbecome apparent to those skilled in the art. It is, therefore, to beunderstood that the appended claims are intended to cover all suchmodifications and variations as fall within the true spirit of theinvention.

What we claim is:
 1. A method of demodulating message symbolstransmitted with synchronization ("sync") symbols, known to thereceiver, differentially encoded over a channel transmitted as symbols sfrom an even symbol constellation during even symbol periods, and as^(s) from an odd symbol constellation during odd symbol periods,comprising the steps of:a) receiving the message and sync symbols; b)calculating initial channel coefficients {h} from the received syncsymbols and the known sync symbols; c) calculating estimated receivedsymbol constellation {Z} comprised of estimated received symbols Z_(ji)which is an estimate of a symbol s_(i) being transmitted during eventime periods through a channel with intersymbol interference from apreviously transmitted symbol ^(s).sbsp.j ; d) calculating estimatedreceived symbol constellation {Z} comprised of estimated receivedsymbols Z_(ji) which is an estimate of a symbol s_(i) being transmittedduring odd time periods through a channel with intersymbol interferencefrom a previously transmitted symbol s_(j) ; e) determining a set ofreference constellation points {Z^(ref) } and {Z^(ref) } being a subsetof estimated received symbol constellations {Z}, {Z} that when rotated,provide received symbol constellations {Z}, {Z}; f) determining apostulated transmitted symbol sequence which would minimize a sum ofbranch metrics, d_(ji), each being a Euclidean distance between receivedmessage symbols and estimated symbol constellation points Z_(ji), Z_(ji)for even and odd symbol periods, respectively; and g) directly updatingreference constellation points {Z^(ref) } and {Z^(ref) } to correct forchanges in the channel over time.
 2. The method of demodulating messagesymbols of claim 1 wherein the reference constellation points {Z^(ref) }and {Z^(ref) } are updated during an even symbol period according to:##EQU18## where Z_(k) ^(ref) (n) is a kth symbol entry of {Z^(ref) }, nis an even integer indicating an even symbol period, k=(i+3j) mod 4, Dis a number of symbol periods since this estimated reference signalconstellation point was last updated, γ is a time constant having avalue between 0 and 1, and the corresponding odd reference constellationpoint is updated from Z_(k) ^(ref) (n) according to: ##EQU19## whereZ_(m) ^(ref) (n) is an mth symbol entry of {Z^(ref) }, {I_(k),Q_(k) }are the real and imaginary components of the estimated reference symbolconstellation points Z_(k) ^(ref) (n).
 3. The method of demodulatingmessage symbols of claim 1 wherein the reference constellation points{Z^(ref) } and {Z^(ref) } are updated during an odd symbol periodaccording to: ##EQU20## where Z_(m) ^(ref) (n) is an mth symbol entry of{Z^(ref) } for n being an odd integer, where m=(i+3j) mod 4; D is thenumber of symbol periods since this estimated reference signalconstellation point was last updated, γ is a time constant having avalue between 0 and 1, and the corresponding reference symbolconstellation point is updated from Z_(m) ^(ref) (n) according to:##EQU21## where Z_(k) ^(ref) (n) is a kth symbol entry of {Z^(ref) },{I_(m),Q_(m) } are the real and imaginary components of the referenceconstellation points Z_(m) ^(ref) (n).